Cooperative Control of Hybrid FES-Exoskeleton: Dynamic Allocation

TL;DR

This work addresses actuator redundancy in hybrid FES-exoskeleton systems for neurorehabilitation by introducing a dynamic allocation framework that modularly distributes real-time torque between FES and the exoskeleton. A high-level shared controller sets the total assistive torque, while a dynamic allocator resolves input redundancy through an allocator equation $\boldsymbol{\tau} = \bar{\boldsymbol{\tau}} + \boldsymbol{g}^*_{\perp} S \boldsymbol{\zeta}$ with $\dot{\boldsymbol{\zeta}} = \boldsymbol{\phi}(\boldsymbol{\zeta}, \bar{\boldsymbol{\tau}}, \boldsymbol{\eta})$, ensuring input-to-state stability and keeping the redistribution invisible to the plant. The FES model combines activation and contraction dynamics ($\tau^{F} = a_{\psi} \tau^{F*}(\theta)$) and is identified via Hammerstein–Wiener methods, enabling a feedforward low-level FES control that respects muscle bandwidth and magnitude constraints. Experimental results on a elbow joint show that dynamic allocation achieves higher tracking accuracy and better adherence to actuator constraints than constant allocation, with a tendency to prioritize FES when its constraints are tighter, reflecting rehabilitation-focused control. The approach offers a modular, real-time solution to actuator redundancy, with potential for clinical deployment, albeit limited by single-joint testing and unmodeled fatigue and sensor noise in allocations.

Abstract

Hybrid assistive systems that integrate functional electrical stimulation (FES) and robotic exoskeletons offer a promising approach for neurorehabilitation. However, control of these systems remains challenging due to actuator redundancy and heterogeneous assistive device constraints. This paper introduces a novel cooperative control architecture based on dynamic allocation to address actuator redundancy in a hybrid FES-exoskeleton system. The proposed approach employs a modular control allocator that redistributes required control torques between FES and exoskeleton actuators in real time, accounting for device-specific limitations and user preferences (e.g., prioritizing one assistive device over another). Within this framework, the high-level controller determines the total assistance level, while the allocator dynamically distributes control effort based on these assistive device-specific considerations. Simulation results and experimental validation demonstrate the method's effectiveness in resolving actuator redundancy in the FES-exoskeleton system while reflecting actuator constraints, indicating its potential for deployment in clinical studies to assess patient acceptance and clinical efficacy.

Figures (6)

• Figure 1: Control architecture of the hybrid FES-exoskeleton system. The proposed dynamic allocation scheme distributes the control torque, determined by the shared control, among the actuators. The adaptation of the cooperative control coefficient is based on the attainable set of both assistive devices. The attainable set of FES-induced control torque, $\mathbb{A}_F$, and attainable set of exoskeleton control torque, $\mathbb{A}_E$, consists of constraints of two actuators. FES-torque model, $\Sigma_F$, and attainable sets of FES, $\mathbb{A}_F$, learned from user data, are used in the low-level FES control and dynamic allocation, respectively.
• Figure 2: Attainable set of FES-induced control torque and exoskeleton torque. Although bandwidth limitations are part of attainable sets $\mathbb{A}_F$ and $\mathbb{A}_E$, this figure only depicts the magnitude constraints of two assistive devices. Note that $\mathbb{A}_F$ on this figure represents the magnitude limitations of FES-induced biceps torque derived from experimental data.
• Figure 3: Simulation results of the dynamic allocation. The allocation considers the attainable sets and constraints (maximum torque magnitude and bandwidth limits) of the actuators when distributing the control effort. Two scenarios are presented, both aiming to maximize FES usage ($80\%$ and $100\%$) within its attainable set. (a) Maximum FES usage within its attainable set. (b) Up to $80\%$ FES assistance within its attainable set.
• Figure 4: Illustration of the hybrid FES-exoskeleton.(a) Only the elbow joint was used to follow a trajectory. (b) The degree is defined so that $0^\circ$ and $90^\circ$ correspond to the elbow angle at which the forearm points downwards and is parallel to the ground, respectively. (c) The FES stimulation is applied to the elbow extensor (triceps brachii) and flexor (brachialis). (d) The F/T sensor is mounted at the interface between the exoskeleton and the user’s forearm, where it measures interaction forces and torques.
• Figure 5: Experimental results of the hybrid FES-exoskeleton system under dynamic allocation.(a) FES activation dynamics indicating actuator bandwidth constraints. (b) FES static torque map representing actuator magnitude saturation. Training data and learned static map for both muscle groups are shown. The static map illustrates both the biceps map (positive $\upsilon$) and triceps map (negative $\upsilon$). (c) Exemplary result demonstrating trajectory tracking, cooperative gain, high-level desired torque $\tau^N$, and desired FES torque $\tau^F$. The green shaded area represents the attainable set of FES torque $\mathbb{A}_F$, derived from the FES torque map in (b) for this specific tracking task. (d) Cooperative gain distribution. (e) Compliance with actuator bandwidth constraints (FES dynamic response in (a)) and magnitude saturation (FES torque map in (b)).

Theorems & Definitions (13)

• Remark 1: Redundancy as an Additional Degree of Freedom
• Remark 2: Nominal Control Input
• Remark 3: FES as One or Two Actuators
• Remark 4
• Theorem 1
• Remark 5: Attainable Sets Represent Actuator Constraints
• Remark 6: User Safety and Comfort Limitations
• Remark 7: Hybrid System Saturation and Anti-Windup
• Theorem 2
• Remark 8: Switching Allocation Dynamics